Strain and Temperature Margin in Nb3Sn Conductors

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Strain and Temperature Margin in Nb3Sn Conductors

• Workshop on Instabilities in Nb3Sn Strands,
  Cables, and Magnets
• April 28-30, 2004
• J.R. Miller, NHMFL

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The NHMFL has (and will continue to be) engaged
in projects requiring state-of-the-art
performance from Nb3Sn superconductors
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The NHMFL 45-T Hybrid
45 T in 32 mm 14 T in 610 mm 16 T max at
windings 100 MJ stored energy
9 W at 1.8 K 15 W at 4.5 K 50 W at 20 K 400 W at
80 K 45 L/h of LHe
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NHMFL 900 MHz
21 T in 105-mm w.b. 40-MJ stored energy 1.8-K
operation
Nb3Sn Coils
HF grade (type 1)
LF grade (type 2)
windings
overbanding
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Next generationSeries-Connected
Hybrid(conceptual)

• 35 T in 40-mm w.b.
• 1 ppm unif. stab.
• 15 T max at s.c. windings
• 30-MJ stored energy

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Especially in these large solenoids, a
quantitative understanding of the strain
sensitivity of Nb3Sn is critical to achieving the
full performance potential of the conductors
this includes achieving the required
stabilityUnderstanding stability requires
understanding both the disturbance spectrum as
well as available margins
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The disturbance spectrumWipf ca. 1975
Space
Point
Distributed
Time
Transient
Joules
Joules/m3
Continuous
Watts
Watts/m3
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Transient disturbances
Point

• Epoxy cracking
• Stick-slip conductor motion
• Flux jumping
• AC losses

Distributed
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Continuous disturbances
Point

• Broken filaments
• Conductor joint
• Heat leak
• AC losses

Distributed
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Flux jumping in conductors with limited cooling
Adiabatic stabilization
Dynamic stabilization
Necessary but not sufficient conditions for
stability
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Flux jumping in conductors with limited cooling
Caveat dynamic stabilization criterion derived
from homogeneous description of multifilamentary
wire, which is strictly applicable only for
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Flux jumping in conductors with limited cooling
Both limits are proportional to
where
These limits are actually relaxed by e gt 0
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External disturbances/limited cooling
For either point or distributed disturbances,
stability margin is essentially proportional to
current-sharing temperature margin, i.e.
With a linear approximation for IC(T),
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IC(e) is well known, including the higher
sensitivity at higher fields
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TC(e) is also well known, but often neglected
because the sensitivity is not as strong as for IC
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Combined in the expression for current-sharing
temperature margin, the effect of strain is more
pronounced, especially at high field
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For our own internal projects, special
characterization facilities have been (and
continue to be) developed
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150-mm Bore Split Solenoid
500 kN loading capability
Up to 15 T with Ho poles 30mm x 70mm rad. access
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Assessment of jacket/strand interaction by wire
and CICC pull tests
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New IC(B,e) setup, under development
assembled probe
IEEE-controlled stepper motor
ramp generator
1.5 kA DC PSU

• Setup to operate in 20 T LBRM at 4.2 K

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Ic(B,e) setup, strain device
sample in G-10 casing
HTS current leads
Cu current pads
wire sample
pull block
Ltap 6 cm Ltot 13 cm
annealed Cu backing and strain gauges
support structure
worm gear assembly

• operating load for device 2 kN
• target sensitivity 1e10-7 V

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20-T Large-Bore Resistive Magnet
200-mm warm bore 170-mm cold bore
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Work is also in progress to establish a firmer
theoretical basis for strain dependence of
critical current
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Nb3Sn Strain Dependence
Strain invariant formulation of Tc Calculation of
Tc including strain dependence Based on physical
model with strong superconductivity Generalization
of deviatoric strain description,
including General tensor treatment of
strain Full range of application Deformation and
hydrostatic strain dependence Asymmetry of strain
dependence
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Nb3Sn Strain Dependence
Formulation allows general applied
strain Longitudinal Transverse Shear Combination C
ombine with mechanical analysis of composite
conductor Effects of matrix on Nb3Sn, Poissons
ratio Relation of transverse stress to strain in
Nb3Sn
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Nb3Sn Strain Dependence
Normalized curve for wire and tape
Calculated absolute values
W.D. Markiewicz, Cryogenics, to be published
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users. How can we help?